Subtracting Vectors

Key Concept:

• Vector subtraction involves subtracting corresponding components of two vectors.

• If x=[x1,x2] and y=[y1,y2], then:
  

x−y=[x1−y1, x2−y2]

• The result is a new vector representing the displacement from y to x

Example: Subtract Vectors x=[2,3] and y=[−4,−2]

1. Given vectors:

• x=[2,3]
• y=[−4,−2]

2. Subtraction formula:

x−y = [x1−y1, x2−y2]

3. Component-wise subtraction:

x−y=[2−(−4),3−(−2)]

4. Simplify:

x−y=[2+4,3+2]=[6,5]

5. Result:

 x−y=[6,5]

Observations:

Subtracting x effectively adds the opposite of y to x.
The result [6,5] represents the displacement vector between
x and y.